Tuesday, December 8, 2020

Cigdem Yirtici, Gendo-Frobenius algebras and comultiplication

Abstract:
Two large classes of algebras, Frobenius algebras and gendo-symmetric algebras, are characterised by the existence of a comultiplication with some special properties. Symmetric algebras are both Frobenius and gendo-symmetric. Kerner and Yamagata investigated two variations of gendo-symmetric algebras and in fact these two variations contain gendo-symmetric and Frobenius algebras. We call one of these variations gendo-Frobenius algebras. In this talk, we construct a comultiplication with some special properties for gendo-Frobenius algebras, which is also a common comultiplication for Frobenius algebras and gendo-symmetric algebras. Moreover, we clarify the differences between Frobenius algebras and gendo-symmetric algebras with respect to comultiplication.